We present millimeter and centimeter wave spectroscopic observations of the H II region NGC 6334A. We have mapped the source in several transitions of CO, CS, and NH3. The molecular emission shows a distinct flattened structure in the east-west direction. This structure is probably a thick molecular disk or torus (2.2 x 0.9 pc) responsible for the bipolarity of the near-infrared (NIR) and radio continuum emission which extends in two "lobes" to the north and south of the shell-like H II region. The molecular disk is rotating from west to east (omega approximately equals 2.4 km/s.pc) about an axis approximately parallel to the radio and NIR emission lobes. By assuming virial equilibrium, we find that the molecular disk contains approximately 2000 solar mass. Single-component gas excitation model calculations show that the molecular gas in the disk is warmer and denser (T(sub k) approximately equals 60 K, n approximately equals 3000/cc) than the gas to the north and south (T(sub k) approximately equals 50 K, n approximately equals 400/cc). High resolution (approximately 5 sec) NH3 (3, 3) images of NGC 6334A reveal several small (approximately 0.1 pc) clumps, one of which lies southwest of the radio continuum shell, and is spatially coincident with a near-infrared source, IRS 20. A second NH3 clump is coincident with an H2O maser and the center of a molecular outflow. The dense gas tracers, CS J = 5 approaches 4 and 7 approaches 6, peak near IRS 20 and the H2O maser, not at NGC 6334A. IRS 20 has a substantial far-infrared (FIR) luminosity L(sub FIR) approximately 10(exp 5) solar luminosity, which indicates the presence of an O 7.5 star but has no detected radio continuum (F(sub 6 cm) < 0.02 Jy). The combination of dense gas, a large FIR luminosity and a lack of radio continuum can best be explained if IRS 20 is a protostar. A third clump of NH3 emission lies to the west of IRS 20 but is not associated with any other molecular or continuum features. The star formation activity in the region has moved west of NGC 6334A to IRS 20 and the H2O maser position. We suggest that NGC 6334A, IRS 20, and the H2O maser spot are part of a "protocluster" of stars which is condensing from the massive molecular disk. The similarity between the structure around NGC 6334A and other large (r approximately 1 pc), massive (M approximately 10(exp 3) solar mass), rotating disks (K3-50A and G10.6-0.4) suggests that this may be a common mechanism by which open clusters form.